Reduce to lowest terms: $- \dfrac{2}{9} \div \dfrac{5}{3} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{5}{3}$ is $ \dfrac{3}{5}$ Therefore: $ - \dfrac{2}{9} \div \dfrac{5}{3} = - \dfrac{2}{9} \times \dfrac{3}{5} $ $ \phantom{- \dfrac{2}{9} \times \dfrac{3}{5}} = \dfrac{-2 \times 3}{9 \times 5} $ $ \phantom{- \dfrac{2}{9} \times \dfrac{3}{5}} = \dfrac{-6}{45} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-6}{45} = \dfrac{-6 \div 3}{45 \div 3} = -\dfrac{2}{15} $